论文信息 - The Error in Linear Interpolation at the Vertices of a Simplex

The Error in Linear Interpolation at the Vertices of a Simplex

A formula for the error in multivariate quasi-interpolation which reproduces the linear polynomials is given. From it sharp pointwise $L_\infty$-bounds for the error in linear interpolation (interpolation by linear polynomials) to function values at the vertices of a simplex are obtained. The corresponding 'envelope theorem' giving the optimal recovery of functions is discussed.

S. Waldron

[1] Interpolation und genaherte Quadratur , 1933 .

[2] Philippe G. Ciarlet,et al. Multipoint Taylor formulas and applications to the finite element method , 1971 .

[3] R. Arcangéli,et al. Sur l'évaluation de l'erreur d'interpolation de Lagrange dans un ouvert de $\mathbb{R}^n$ , 1976 .

[4] T. J. Rivlin,et al. The optimal recovery of smooth functions , 1976 .

[5] K. Chung,et al. On Lattices Admitting Unique Lagrange Interpolations , 1977 .

[6] Charles A Micchelli,et al. A Constructive Approach to Kergin Interpolation in R(k). , 1978 .

[7] Yu. N. Subbotin. Error of the approximation by interpolation polynomials of small degrees on n-simplices , 1990 .

[8] A multivariate form of Hardy's inequality and L p -error bounds for multivariate Lagrange interpolation schemes , 1997 .

[9] Shayne Waldron,et al. Multipoint Taylor formulæ , 1998, Numerische Mathematik.